Could anyone please tell me a relatively short approach on how to find equation of a plane if I'm given it is at equal distance from 2 given lines.... I tried finding the the equation of the line perpendicular to both the lines and hence the corresponding points on the both the lines and then using distance formula to equate the distance of a point (x, y, z) from both the points and then simplifying it... But I find the method(I'm not even sure if it's correct) very very long.. So it would be really helpful if anyone could suggest a short method for this one..
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could you give an example of your work? – user Jan 27 '18 at 17:35
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Step 1: the vector normal to the plane must be normal to direction vectors of both lines – so it is paralel to their vector product. – CiaPan Jan 27 '18 at 18:06
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Step 2: the plane halves any line segment, whose endpoins belong to both lines. Of course both hints apply if your given lines ar not parallel...! – CiaPan Jan 27 '18 at 18:10
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Do the hints apply even if the lines aren't skew... That is even if they intersect? – rohit_r Feb 23 '18 at 13:41